The insects are a great nuisance . . . . . . . . us. A. for B. at C. with D. to

The correct answer is: to.

The preposition “to” is used to indicate the person or thing that is affected by an action. In this case, the insects are affecting us by being a nuisance.

The other options are incorrect because they do not make sense in the context of the sentence.

• “For” is used to indicate the purpose of an action. In this case, the insects are not acting for any purpose, they are simply being a nuisance.
• “At” is used to indicate a location or direction. In this case, the insects are not located at us, they are around us.
• “With” is used to indicate possession or association. In this case, the insects are not associated with us, they are simply bothering us.